Phantom Axe does not come with Pride, it is Elaborate/Exceed.
Again, because of this, you have 8 Assault weapons, Phantom Axe and your Soul weapon. This is roughly +-0 compared to having 9 Assault weapons and a Soul weapon.
Meanwhile, with Lance/Hammer/Glaive/Bow Grid have 9 Assault weapons, plus the Phantom weapon and the Soul weapon. So you gain an extra weapon slot - kind of.